When the notorious Logan Paul launched his Twitch channel last month, the streaming platform’s moderators were ready.

“We wanted to have control of the chat from the very beginning,” said “Kanthes,” a freelance moderator who chose not to use his real name when he told Polygon all about moderating Paul’s first Twitch stream.

Paul, of course, initially gained recognition on YouTube, where he’s had a rocky start to 2018. Though he’s still active on the video platform (it’s...